To convert the fraction 13/20 to a decimal using long division, follow these steps:
1. Divide 20 by 13. Write the quotient (1) above the division bar.
```
1
โโโโโโ
13โ20
13
```
2. Multiply the quotient (1) by the divisor (13) and subtract the result from the dividend (20).
```
1
โโโโโโ
13โ20
13
โโ
7
```
3. Bring down the next digit of the dividend (0).
```
1
โโโโโโ
13โ20
13
โโ
7
+0
```
4. Divide the new dividend (70) by the divisor (13). Write the quotient (5) above the division bar.
```
1 5
โโโโโโ
13โ20
13
โโ
7
+0
65
```
5. Multiply the quotient (5) by the divisor (13) and subtract the result from the new dividend (70).
```
1 5
โโโโโโ
13โ20
13
โโ
7
+0
65
โโ
5
```
6. Bring down the next digit of the dividend (0).
```
1 5
โโโโโโ
13โ20
13
โโ
7
+0
65
โโ
5
+0
```
7. Divide the new dividend (50) by the divisor (13). Write the quotient (3) above the division bar.
```
1 5 3
โโโโโโโโ
13โ20
13
โโ
7
+0
65
โโ
5
+0
52
```
8. Multiply the quotient (3) by the divisor (13) and subtract the result from the new dividend (50).
```
1 5 3
โโโโโโโโ
13โ20
13
โโ
7
+0
65
โโ
5
+0
52
โโ
-2
```
9. Since the remainder is negative, we can add a decimal point and a zero to the dividend and continue the division.
```
1 5 3
โโโโโโโโ
13โ20.0
13
โโ
7
+0
65
โโ
5
+0
52
โโ
-2.0
```
10. Divide the new dividend (โ20) by the divisor (13). Write the quotient (โ1) above the division bar.
```
1 5 3 โ1
โโโโโโโโโโโโ
13โ20.0
13
โโ
7
+0
65
โโ
5
+0
52
โโ
-2.0
-1
```
11. Multiply the quotient (โ1) by the divisor (13) and subtract the result from the new dividend (โ20).
```
1 5 3 โ1
โโโโโโโโโโโโ
13โ20.0
13
โโ
7
+0
65
โโ
5
+0
52
โโ
-2.0
-1
13
```
12. Bring down the next digit of the dividend (0).
```
1 5 3 โ1
โโโโโโโโโโโโ
13โ20.0
13
โโ
7
+0
65
โโ
5
+0
52
โโ
-2.0
-1
13
+0
```
13. Divide the new dividend (โ70) by the divisor (13). Write the quotient (โ5) above the division bar.
```
1 5 3 โ1 โ5
โโโโโโโโโโโโโโ
13โ20.0
13
โโ
7
+0
65
โโ
5
+0
52
โโ
-2.0
-1
13
+0
-65
```
14. Multiply the quotient (โ5) by the divisor (13) and subtract the result from the new dividend (โ70).
```
1 5 3 โ1 โ5
โโโโโโโโโโโโโโ
13โ20.0
13
โโ
7
+0
65
โโ
5
+0
52
โโ
-2.0
-1
13
+0
-65
โโโโ
-50
```
15. Bring down the next digit of the dividend (0).
```
1 5 3 โ1 โ5
โโโโโโโโโโโโโโโโ
13โ20.0
13
โโ
7
+0
65
โโ
5
+0
52
โโ
-2.0
-1
13
+0
-65
โโโโ
-50
+ 0
```
16. Divide the new dividend (โ500) by the divisor (13). Write the quotient (โ38) above the division bar.
```
1 5 3 โ1 โ5 โ38
โโโโโโโโโโโโโโโโโโโโ
13โ20.0
13
โโ
7
+0
65
โโ
5
+0
52
โโ
-2.0
-1
13
+0
-65
โโโโ
-50
+ 0
-39
```
17. Multiply the quotient (โ38) by the divisor (13) and subtract the result from the new dividend (โ500).
```
1 5 3 โ1 โ5 โ38
โโโโโโโโโโโโโโโโโโโโ
13โ20.0
13
โโ
7
+0
65
โโ
5
+0
52
โโ
-2.0
-1
13
+0
-65
โโโโ
-50
+ 0
-39
-39
```
18. Since the remainder (-390) is a multiple of the divisor (13), the long division is complete.
The fraction 13/20 as a decimal is approximately 0.65.